TITLE: Four-parameter Beta distribution and Wikipedia
QUESTION [6 upvotes]: Sorry if it is not an appropriate place for such questions, but anyway can anybody please confirm that the formula for the density function of the four-parameter Beta distribution is correct in Wikipedia. It seems $(c - a)$ is missing in the denominator. Thank you.
Best regards,
Ivan

REPLY [5 votes]: Yes, the factor is indeed missing. 
Let $X$ be standard 2-parameter Beta random variable. The four-parameter one $Y$ is obtained by affine transformation $Y = (c-a) X + a$ for $c>a$. Then
$$
   f_Y(y) = \frac{1}{c-a} f_X\left(\frac{y-a}{c-a}\right) = \frac{1}{c-a} \left(\frac{y-a}{c-a} \right)^{\alpha-1} \left(\frac{c-y}{c-a} \right)^{\beta-1} \frac{\mathbf{1}(a < y <c)}{B(\alpha,\beta)} = 
   \frac{(y-a)^{\alpha-1} (c-y)^{\beta-1}}{(c-a)^{\alpha+\beta-1}}\frac{\mathbf{1}(a < y <c)}{B(\alpha,\beta)}
$$